The French president, Emmanuel Macron, has set out his plans for a “profound transformation” of the EU with deeper political integration to win back the support of disgruntled citizens, but suggested a bloc moving forward at differing speeds could become somewhere the UK may “one day find its place again”.

Macron, a staunchly pro-European centrist who came to power in May after beating the Front National’s Marine Le Pen, pleaded for the EU to return to its founders’ “visionary” ideas, which were born out of the disaster of two world wars.

In what was hailed on Tuesday as one of the most pro-European speeches by an EU leader in years, he spoke up for common EU policies on defence, asylum and tax, called for the formation of European universities, and promised to play Ode to Joy, the EU anthem, at the Paris Olympics in 2024.

With Brexit looming, Macron warned the rest of Europe against the dangers of anti-immigrant nationalism and fragmentation. “We thought the past would not come back … We thought we had learned the lessons,” he told a crowd of European students at Sorbonne University in Paris.

Days after a far-right party entered the German parliament for the first time in 70 years, Macron said an isolationist attitude had resurfaced “because of blindness … because we forgot to defend Europe. The Europe that we know is too slow, too weak, too ineffective”.

Macron said he was deliberately not saying much about Brexit in his speech, but a reinvigorated EU with various levels of integration and cooperation was somewhere the UK may “one day find its place again”. He left the suggestion deliberately vague.

Macron’s proposals included shoring up the 19-member eurozone with a finance minister, budget and parliament – ideas dependent on the backing of Berlin. Major reform of the eurozone risks being curtailed by conservatives in Angela Merkel’s new coalition government, which is yet to be formed.

Even before the German federal election, Berlin had ruled out euro bonds – shared borrowing across the eurozone. Germany also puts more emphasis on enforcing financial rules in its discussions about a European monetary fund, a vehicle to replace the existing bailout mechanism.

Q&A

Why do some states oppose deeper EU integration?

In the eurosceptic imagination there is a place called Brussels that issues diktats about straight bananas and European armies. In reality, there are 28 European Union member states, soon to be 27, with a smorgasbord of political traditions and priorities.

The breadth of EU membership explains why the depth of integration is always contested. In theory, 27 countries (excluding Britain) agree on the priorities for the next decade: stronger eurozone institutions to protect the single currency, joined-up action on migration and defence, a free-trading continent that is not “naive” about foreign competition. The difficulty is they do not agree how to get there. Take the eurozone: France and Germany agree on further integration, including a eurozone finance minister and European monetary fund, but disagree on how much risk should be shared. Or migration: every EU member state wants more “solidarity”. Solidarity for Italy and Greece means other countries taking in more refugees. Solidarity for Hungary means tougher action to protect the EU’s external borders.

For most countries, tax and military spending are closely tied up to national sovereignty, so there is reluctance to cede too much control to EU processes. Europe has always been about compromise. But compromises can be harder to find in a bigger club.

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Macron acknowledged these concerns in his speech, saying eurozone reform was “not about mutualising our past debts or solving the financial problems of one country”. In a defiant message to Germany’s pro-business Free Democratic party, which could come into coalition with Merkel and warned of “red lines” this week, Macron said: “I don’t have red lines, I only have horizons.”

To reduce inequalities across the EU, Macron suggested greater harmonisation of tax policies, including taxing technology companies such as Facebook and Apple where they make money rather than where they are registered.

Macron also proposed that every EU country should guarantee a minimum wage and payroll charges. “I believe deeply in this innovation economy,” he said. However, Macron added, “we must have this debate” about making taxation fairer.

He vowed to revive the French-backed project of a financial transaction tax to fund overseas aid – an idea that has never got off the ground since it was proposed in the aftermath of the financial crisis.

On defence, Macron called for a Europe-wide “rapid-reaction force” to work with national armies and “a common strategic culture” of a joint European defence budget and policy, ideas already under discussion but in the early stages. He suggested the creation of a European intelligence academy to better fight against terrorism, and a joint civil protection force.

On the migration crisis, Macron said: “Making a place in Europe for refugees who have risked their life is our duty.” He pushed for a closer common asylum policy, currently a work in progress that has been criticised for failures. Macron also suggested a European asylum agency and standard EU identity documents.

Macron addresses students at Sorbonne University. He touched on the many areas of his EU vision in the speech. Photograph: Ludovic Marin/Reuters

The French president said the EU needed to encourage “radical” digital innovation to compete internationally.

In farming, he suggested he may be willing to challenge French shibboleths by pledging reform of the common agricultural policy, which has historically been defended by France and its powerful agricultural lobbies.

He did not neglect the nitty-gritty of EU institutions, repeating his support for transnational MEPs and throwing his weight behind plans to limit the European commission to 15 members, down from the “one country, one commissioner” quota that has blocked change.

Macron called for the creation of European universities and said that by 2024, all European students should be able to speak at least two European languages.

Maria Demertzis, the deputy director of the Bruegal thinktank, said Macron had been very cautious on eurozone reform, which reflected German reality. “His speech touches on areas where there is very little disagreement – defence, security, sustainable development, the young, education, research,” she said.

“This type of thing, everyone agrees on the need to do more. On the eurozone reform, there is no agreement on this. For a eurozone budget to make a difference, if it is a small budget we are back to square one.”

Some ideas were traditional French priorities, such as an EU carbon tax on exports from countries with lower environmental standards. Previous French presidents, such as Nicolas Sarkozy, pursued this idea, but lost out to the EU’s preferred option of a carbon-trading scheme.

The speech was received warmly by the European commission president, Jean-Claude Juncker. “A very European speech from my friend Emmanuel Macron,” he tweeted.

“What we need now is a roadmap to advance the union at 27. We have to openly discuss all ideas and decide before May 2019,” Juncker said, referring to a summit he wants Romania to host on 30 March 2019, the day after Britain leaves the EU.

In early December, the commission will publish proposals for a eurozone finance minister and other reforms. EU leaders will discuss the ideas at a summit later that month.